V.9:3 (131-132): Fourier Analyses by John Sweeney

Fourier Analyses by John Sweeney

One of the fascinating ideas that came up early in STOCKS & COMMODITIES' days was the Fourier analyses applied to stock and commodity data by Anthony Warren and Jack Hutson (see Technical Analysis of STOCKS & COMMODITIES, Volume 1). While this technique has its limitations for forecasting, it's great for seeing what cyclical content there is in your price data. Given this, you can detrend the data and select the "correct" length of trend-following indicators, whether they are averages, cycles or whatever (''filters'' to you engineers). Practically speaking, it helps you find a line that will cut the price charts' curves as the right point in a turnaround. For example, in Figure 1, you don't want line A's behavior or necessarily line C's. You'd like line B's. This analysis helps find the appropriate curve, plus these graphs also give you an idea of the relative importance of the many cycles inherent in your data.

Take Figure 2, for example. This is an amplitude (vertically) vs. frequency (horizontally) chart of the cyclical content for December Euros, October 1989 to December 1990. The first point to notice is the "regularity" of the peak and cycle information. The data aren't "smeared" across the chart, either horizontally or vertically, and the amount of space between peaks and valley is fairly regular, which I want because I'd like to find some relationships between each cycle length and its harmonics at half, quarter and eighth lengths. The data aren't perfectly clean — this is the real world — so, for example, eight days is not half of 14 days, which is not half of 22 days, and so on. In this case, the sharpness of the peaks and the regularity of the lengths is reassuring.